The pion-nucleon σ term from pionic atoms

Earlier work suggested that the in-medium πN threshold isovector amplitude b ₁ (ρ) gets renormalized in pionic atoms by ∼30% away from its ρ=0 free-space value, relating such renormalization to the leading low-density decrease of the in-medium quark condensate <q¯q> and the pion decay constant f _π in terms of the pion-nucleon σ term σ _πN . Accepting the validity of this approach, we extracted σ _πN from a large-scale fit of pionic-atom level shift and width data across the periodic table. Our fitted value σ _πN =57±7 MeV is robust with respect to variation of πN interaction terms other than the isovector s-wave term with which σ _πN was associated. Higher order corrections to the leading order in density involve some cancellations, suggesting thereby only a few percent overall systematic uncertainty. The value of σ _πN derived here agrees with values obtained in several recent studies based on near-threshold πN phenomenology, but sharply disagrees with values obtained in recent direct lattice QCD calculations.